Question

given the figure below, find the values of x and z. (5x - 13)° (9x - 73)° x = z =

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, $9x - 73=5x - 13$.

Step2: Solve the equation for x

Subtract $5x$ from both sides: $9x-5x - 73=5x-5x - 13$, which simplifies to $4x-73=-13$. Then add 73 to both sides: $4x-73 + 73=-13 + 73$, giving $4x = 60$. Divide both sides by 4: $x=\frac{60}{4}=15$.

Step3: Find the value of one of the angles

Substitute $x = 15$ into $5x-13$: $5\times15-13=75 - 13=62$.

Step4: Use the linear - pair property to find z

The angle $(5x - 13)$ and $z$ form a linear - pair, so $(5x - 13)+z = 180$. Since $5x - 13 = 62$, then $z=180 - 62=118$.

Answer:

$x = 15$
$z = 118$